Question

For the function g(t)= 10(0.62)^t determine the following values.The initial value:10The 1-unit growth factor:The 2-unit growth factor: The 2-unit percent change:The 1/2-unit growth factor:The 1/2-unit percent change:

Answer 1

Given:

$g\mleft(t\mright)=10\mleft(0.62\mright)^t$

To find the 1-unit growth factor:

Put t=1 in the given function

We get

$\begin{gathered} g\mleft(t\mright)=10\mleft(0.62\mright)^1 \\ =10(0.62) \\ =6.2 \end{gathered}$

Hence, the answer is 6.2.

To find the 2-unit growth factor:

Put t=2 in the given function

We get

$\begin{gathered} g\mleft(t\mright)=10\mleft(0.62\mright)^2 \\ =10(0.62)^2 \\ =3.844 \end{gathered}$

Hence, the answer is 3.844.